Tidal Disruption of Planetesimals from an Eccentric Debris Disk Following a White Dwarf Natal Kick

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2024-05-09 18:00:04

White dwarfs are the remnants of stars with main-sequence masses below 8 M☉, which constitute an estimated 97% of stars in our Galaxy—including our Sun (Fontaine & Wesemae2000). White dwarfs are extremely dense bodies with masses comparable to the Sun, despite their sizes being closer to that of the Earth (Schatzman 1958). Most white dwarfs should have a core of carbon and oxygen surrounded by a thin, outer layer of hydrogen and helium (Burbidge & Burbidge 1954). However, an estimated 25%–50% of observed white dwarfs show signs of metals such as calcium, magnesium, iron, and silicon in their spectra (e.g., Zuckerman et al. 2003, 2010; Koester et al. 2014). Metal-polluted white dwarfs are found with a wide range of effective temperatures 3000–25,000 K (see Farihi 2016) with estimated cooling ages as old as 10 Gyr (Elms et al. 2022).The presence of metals in white dwarf spectra is commonly attributed to the active accretion of planetary material following a tidal disruption event (e.g., Debes & Sigurdsson 2002; Jura 2003; Wang et al. 2019; Brouwers et al. 2022), given that any surface metals should sink to the core on a timescale much shorter than the white dwarf age through gravitational settling (see Jura & Young 2014). The radius at which this tidal disruption occurs is the white dwarf's Roche radius ≈1 R☉ (e.g., Li et al. 1998; Davidsson 1999; Bear & Soker 2013; Veras et al. 2014; Barber et al. 2016; Veras 2021). Once a planetesimal is tidally disrupted, the bound planetary debris forms a circumstellar disk, which produces an observable infrared excess (e.g., Jura 2003; Jura et al. 2007), and many white dwarfs have been found with surrounding planetary material in this manner (Farihi 2016). The composition of tidally disrupted planetesimals can be inferred from metal abundances on polluted white dwarfs, which provides a unique avenue for the study of exoplanet compositions (e.g., Zuckerman et al. 2007, 2010; Koester et al. 2014).Estimated mass accretion rates are high and challenging to explain (e.g., Brouwers et al. 2022). Time-averaged accretion rates inferred from helium white dwarfs are typically 1 × 109 g s−1, whereas instantaneous accretion rates measured from hydrogen white dwarfs are around 1 × 107 g s−1 (Farihi et al. 2012; Hollands et al. 2018; Blouin & Xu 2022). The highest rates inferred from helium and hydrogen white dwarfs are approximately 1 × 1011 g s−1 and 1 × 109 g s−1, respectively (e.g., Dufour et al. 2012; Gänsicke et al. 2012; Xu et al. 2013; Farihi et al. 2016; Cunningham et al. 2022). There are many proposed mechanisms for the tidal disruption of planetesimals, including perturbations due to secular resonances (Smallwood et al. 2018), binary stellar companions (e.g., Bonsor & Veras 2015; Hamers & Portegies Zwart 2016), secular instabilities triggered by planetary engulfment (Petrovich & Muñoz 2017), and mass loss on the asymptotic giant branch (Reimers 1975; Bloecker 1995; Bonsor et al. 2011). Exomoons (e.g., Trierweiler et al. 2022) and planets (e.g., Frewen & Hansen 2014) have also been proposed as potential sources of pollution in addition to asteroids and comets.As a main-sequence star with mass below 8 M☉ runs out of hydrogen in its core, it turns into a red giant star to undergo subsequent fusion of heavier elements (Iben 1967). On the asymptotic giant branch, the outer layers of the star become unbound, and about half of the stellar mass is lost before the core collapses into a white dwarf (Auer & Woolf 1965; Fusi-Pecci & Renzini 1976). When this mass ejection occurs anisotropically, a natal kick is imparted on the white dwarf upon its formation (Fellhauer et al. 2003). The kick magnitude is expected to be 1 to 3 km s−1 (e.g., Fregeau et al. 2009; El-Badry & Rix 2018; Hamers & Thompson 2019); the direction of the kick with respect to the planetesimal disk plane is unknown. Stone et al. (2015) considered the effect of this natal kick on exo-Oort clouds. The kick maps many comets onto radial, plunging orbits, which produces a temporary burst of tidal disruption events. However, their Monte Carlo approach followed postkick orbits on a short timescale without self-gravity, and hence does not apply to the cooler population of metal-polluted white dwarfs. In this Letter, we show that the white dwarf natal kick results in the formation of an apse-aligned, eccentric debris disk of planetesimals, which produces tidal disruption events at a rate consistent with observed mass accretion rates for 100 Myr.

When a gravitational recoil kick is imparted on a supermassive black hole, the surrounding stellar orbits in a nuclear star cluster can form an eccentric, apse-aligned disk (Akiba & Madigan 2021, 2023), and these eccentric disks exhibit stellar tidal disruption rates as high as 0.1 yr−1 gal−1, 3 to 4 orders of magnitude higher than rates expected from isotropic distributions (Madigan et al. 2018a). The dynamics work on all scales in a near-Keplerian system and thus are directly applicable to planetesimals surrounding white dwarfs following the impartment of a natal kick. To quantify apsidal alignment, we make use of the eccentricity vector where v is the velocity vector, j is the (specific) angular momentum vector, M* is the white dwarf mass, and is the unit position vector. The eccentricity vector points from the apoapsis to the periapsis of a given orbit, with a magnitude equal to the scalar eccentricity.The mean eccentricity vector is a measure of apsidal alignment defined by where e i is the eccentricity vector of the i-th planetesimal and N is the number of planetesimals considered. When the white dwarf experiences an in-plane kick, planetesimals on initially circular orbits will align their eccentricity vectors such that where vkick is the natal kick speed and vcirc is the initial circular speed of the planetesimals. Apsidal alignment is strongest when ∣〈 e 〉∣ = 1. From Equation (3), this occurs at a characteristic radius For M* = 0.6 M☉ and vkick = 1 km s−1, this radius occurs at rc = 240 au. For vkick = 3 km s−1, rc = 30 au.In the solar system, an orbital distance of 30 au corresponds to that of Neptune and the Kuiper Belt, a dynamically rich region of space that includes both kinematically cold and hot primordial planetesimal populations intermixed with those in orbital resonance with Neptune (e.g., Jewitt & Luu 1993; Malhotra 2019). A distance of 240 au corresponds to that of the scattered disk, a population of planetesimals on eccentric orbits with periapses that bring them into contact with Neptune's orbit (Duncan & Levison 1997; Vokrouhlický & Nesvorný 2019). We note that this comparison does not take into account orbital expansion due to the star's mass loss (e.g., Veras et al. 2013). The existence of Kuiper Belt or scattered disk-like structures in exoplanet systems has been inferred from observations (e.g., Geiler et al. 2019; Wyatt 2020); disks of icy bodies in the outskirts of planetary systems should be common.Dynamical stability in eccentric disks comes about via mutual gravitational torques between orbiters (Madigan et al. 2018a). When a planetesimal precesses ahead of the eccentric disk, its orbit is negatively torqued by the disk, and its angular momentum decreases, which in turn increases its scalar eccentricity. This change in eccentricity works to slow down the orbit's precession and allows the rest of the disk to catch up to it. The opposite is true for an orbit that lags behind the disk: it feels a positive torque, which circularizes the orbit and increases its precession speed. In this way, the eccentric disk maintains its apsidal alignment as individual orbits undergo oscillations in precession speeds and eccentricity. It is the latter oscillation in eccentricity that causes an enhancement in the rate of tidal disruption events as strong mutual torques throw planetesimals onto radial, star-grazing orbits.

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